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- W4295995429 abstract "A quantitative evaluation for shock-capturing over-amplification errors is provided to characterize the performance of shock-capturing schemes. Following our previous work on solely discontinuities, now we account for the concurrent presences of discontinuities and smooth waves, each with a complete set of supported modes on a given grid. The linear advection equation is taken as the model equation, and a standardized error evaluation is given for overshooting oscillations produced by shock-capturing schemes in the numerical solutions. Therefore, we can quantitatively reveal the shock-capturing robustness of, for example, the well-known high-order WENO schemes, by comparing and analysing the resulting numerical overshoots. In particular, we are able to find out the ranges of wavenumbers in which the numerical schemes are especially prone to produce overshoots. While lower-dissipation is usually expected for high-order schemes, we eventually provide a simple measure for quantifying the shock-capturing robustness, which was not a trivial task due to the nonlinearity and complexity of shock-capturing computations." @default.
- W4295995429 created "2022-09-16" @default.
- W4295995429 creator A5053447705 @default.
- W4295995429 date "2022-08-04" @default.
- W4295995429 modified "2023-09-26" @default.
- W4295995429 title "Improving the quantification of overshooting shock-capturing oscillations" @default.
- W4295995429 doi "https://doi.org/10.48550/arxiv.2208.02853" @default.
- W4295995429 hasPublicationYear "2022" @default.
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